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Question
If A = 7x2 + 5xy − 9y2, B = −4x2 + xy + 5y2 and C = 4y2 − 3x2 − 6xy then show that A + B + C = 0.
Solution
A = 7x2 + 5xy − 9y2
B = −4x2 + xy + 5y2
C = 4y2 − 3x2 − 6xy
Substituting the values of A, B and C in A+B+C:
= (7x2 + 5xy − 9y2)+(−4x2 + xy + 5y2)+(4y2 − 3x2 − 6xy)
= 7x2 + 5xy − 9y2−4x2 + xy + 5y2+4y2 − 3x2 − 6xy
Rearranging and collecting the like terms:
(7-4-3)x2 + (5+1-6)xy +(−9+5+4)y2
= (0)x2 + (0)xy + (0)y2
= 0
⇒A+B+C=0
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